STAT4290 April 29 2011

STAT4290 April 29 2011 - tailed test Technical point: On...

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The exact null distributions of D, D+, D- can be found by considering all orderings of the Xs and Ys, which should be equally likely under Ho. Calculate the test statistic for each ordering build up the empirical distribution. Quantiles of the null distribution are give in TABLE A19 for n = m and A20 for n ≠ m So: for the two-sided test, reject Ho if D is greater than the 1-α quantile for a two-sided test, from Table A19 or A20. For the one-sided tests, reject Ho if D+ ( or D-) is greater than the 1-α quantile for a one-sides test. Note: IF m=n (and only in that case!) we can get an exact one-sided p-value: + ( ), = , - 2nn nd 2nn d observed value of test statistic double this for a two
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Unformatted text preview: tailed test Technical point: On terms of the actual mechanics of the test, the difference between S1(z) and S2(z) changes only at the observed vales z = Xi and z = Yi. So its enough to calculate S1(z)-S2(z) just at the observed data points. Another way of comparing the distributions of two samples is the Cramer-von Mises test . The setup is the same as before an independent sample of n observations X1,X2,X3,Xn and another independent sample of m observations Y1,Y2,Ym. S1 and S2 are the edfs. Test statistic: = + = =-V mnm n2 x Xix YiS1x S2x2 (note: Sum of the square deviations should be small if the samples come from the same distribution!)...
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